A CT scanner includes an x-ray tube mounted on a rotatable gantry that rotates around an examination region about a z-axis. A detector array subtends an angular arc opposite the examination region from the x-ray tube. The x-ray tube emits radiation that traverses the examination region. The detector array detects radiation that traverses the examination region and generates projection data indicative thereof. A reconstructor processes the projection data using an iterative or non-iterative reconstruction algorithm and generates volumetric image data indicative of the examination region. The volumetric image data does not reflect the spectral characteristics as the signal output by the detector array is proportional to the energy fluence integrated over the energy spectrum.
A CT scanner configured for spectral CT has included a single broad spectrum x-ray tube and an energy-resolving detector array with energy-resolving detectors (e.g., with photon counting detectors, at least two sets of photodiodes with different spectral sensitivities, etc.) and discrimination electronics, a single x-ray tube configured to switch between at least two different emission voltages (e.g., 80 kVp and 140 kVp) during scanning, or two or more x-ray tubes configured to emit radiation having different mean spectra. A signal decomposer decomposes the energy-resolved signals into various energy dependent components, and a reconstructor reconstructs the individual components, generating volumetric image data that reflects the spectral characteristics.
Reconstruction techniques have included filtered back-projection, statistical iterative image reconstruction, etc. An example statistical iterative image reconstruction algorithm has been based on a cost function, which includes a data fidelity term and an image noise penalty term. A general formulation of such a cost function is: Cost(x)=−L(Ax|y)+β·R(x), where Cost(x) represents the cost function, L(Ax|y) represents a likelihood term that compares a forward projected image (Ax, where A is a forward projection operator and x is the image) to measured data (y), R(x) represents a roughness penalty term that penalizes noise (or “roughness”) in the reconstructed image (x), and β represents a regularization term that controls a strength of the regularization.
With the above iterative image reconstruction formulation, in particular if the roughness penalty contains only linear or quadratic terms of the voxel values, voxels representing sharp edges (e.g., bone) and low contrast structure (e.g., soft tissue) are similarly smoothed. For example, with a current state of the art approach, a final image noise level is typically used (e.g., decrease image noise by 30%) to determine the regularization parameter β that provides a uniform decrease in noise across the image. Spectral images are separately reconstructed, and then combined, through a linear combination, to produce an image for display. With the above iterative image reconstruction formulation, the spectral images may have similar noise; however, there is no guarantee that they will have a similar spatial resolution, and, unfortunately, a linear combination of spectral images having different spatial resolution may introduce artifact and/or have incorrect quantitative values.